[en] A 10.24-day Neptune-mass planet was recently announced as orbiting the nearby M2 dwarf Gl 176, based on 28 radial velocities measured with the HRS spectrograph on the Hobby-Heberly Telescope. We obtained 57 radial velocities of Gl 176 with the ESO 3.6 m telescope and the HARPS spectrograph, which is known for its sub-m s[SUP]-1[/SUP] stability. The median photon-noise standard error of our measurements is 1.1 m s[SUP]-1[/SUP], significantly lower than the 4.7 m s[SUP]-1[/SUP] of the HET velocities, and the 4-year period over which they were obtained overlaps considerably with the epochs of the HET measurements. The HARPS measurements show no evidence of a signal at the period of the putative HET planet, suggesting that its detection was spurious. We do find, on the other hand, strong evidence of a lower mass 8.4 M_Earth planet, in a quasi-circular orbit and at the different period of 8.78 days. The host star has moderate magnetic activity and rotates on a 39-day period, which we confirm through modulation of both contemporaneous photometry and chromospheric indices. We detect that period, as well, in the radial velocities, but it is well removed from the orbital period and offers no cause for confusion. This new detection of a super-Earth (2 M_Earth < M sin (i) < 10 M_Earth) around an M dwarf adds to the growing evidence that such planets are common around very low-mass stars. A third of the 20 known planets with M sin (i)< 0.1 M_Jup and 3 of the 7 known planets with M sin (i) < 10 M_Earth orbit an M dwarf, in contrast to just 4 of the ~300 known Jupiter-mass planets. Based on observations made with the HARPS instrument on the ESO 3.6-m telescope at La Silla Observatory under program ID 072.C-0488.